I know of ESXi as virtual host in VMware workstation or VMware fusion,etc...
However in Production environments I am not aware of that.. just heard about it...
I thought if ESXi can be installed as virtual on the SAN, that might save Admins from the cumbersome wiring.

I heard about ESXi that boots from the SAN, but the resources CPU/RAM still get provisioned from ESXi physical server...

As Andrew rightly mentioned, The Nested ESXi is only for the purpose of labs. I have an environment with nested ESXi which i use for my training.
ESXi is a bare metal Hypervisor. The fact that they let you put it on virtual machine is only for experimental purposes.
That's the reason you will not directly find ESXi on the OS list. Only after you finish creating a VM, you will be able to find it by going to edit settings>OS options.
This is what it says when you choose it.

Virtualization software lets you run different versions of Windows, Ubuntu Linux and other versions of Linux all at the same time, rather than running each one directly from your computer's hard drive.

This tutorial will walk an individual through the steps necessary to enable the VMware\Hyper-V licensed feature of Backup Exec 2012. In addition, how to add a VMware server and configure a backup job.
The first step is to acquire the necessary licen…

This Micro Tutorial walks you through using a remote console to access a server and install ESXi 5.1. This example is showing remote access and installation using a Dell server. The hypervisor is the very first component of your virtual infrastructu…